Jonathan Taylor (UP)
Since Renault's reconstruction of Cartan pairs as (twisted) groupoid C*-algebras, later generalisations of the theory have partially diverged. Staying in the realm of C*-algebras with a 'large' commutative subalgebra, there are (at least) two generalisations: weak Cartan pairs and essential Cartan pairs. Both of these definitions then admit reconstruction theorems utilising competing definitions of an "essential groupoid C*-algebra", and it is currently not known whether these two definitions differ.
In talk I will describe the similarities and differences between these two definitions of essential groupoid C*-algebras, and the approaches and techniques of which they make use.
